Halftoning involves rendering continuous tone (“contone”) digital grayscale and color images as patterns of pixels that can be displayed by printers and other display devices having a limited number of display colors. The rendered images are commonly referred to as halftone images. The pixels of a halftone image are arranged in patterns such that the halftone image is perceived as having continuous tones when viewed through the human visual system.
As applied to printing, Frequency Modulation (“FM”) halftoning involves varying the number or density of ink dots in an area to achieve a tone. The ink dots are isolated and have uniform size. The human visual system perceives areas of the FM halftone image having a greater density of dots to be darker than areas having a lower dot density.
Laser printers and some other image forming devices do not stably or reliably produce isolated dots beyond a certain horizontal dot resolution. For example, some laser printers operate in an enhanced resolution imaging mode, sometimes referred to as a High Definition Imaging (HDI) mode. In HDI mode, the laser horizontal scan line of the normal resolution mode is subdivided into finer increments, whereby the laser printer produces dots during correspondingly shorter laser on/off cycles. For example, if the normal horizontal resolution mode of a laser printer is 600 dots per inch (dpi), and the enhanced horizontal resolution mode of that laser printer is 2,400 dpi, then each pixel of the halftone image produced by that laser printer in HDI mode is subdivided into four sub-pixels, so that the laser on/off cycle in the HDI mode is ¼th the laser on/off cycle in the normal horizontal resolution mode. Such dot instability can result in perceptible visual anomalies or quantization noise in the resulting halftone image produced by the laser printer. Dot dropouts can occur in highlights, plugging can occur in shadows, and grainy appearances due to dot clumping in mid-tones can occur.
Dot instability can be reduced by clustering the dots. Conventional dot clustering involves using periodic arrangements of pixel clusters on a grid that provides stable dot transfer. Tones can be made darker by making the clusters larger. The pattern power spectra of the clustered dots exhibits a strong mid-frequency component, as opposed to the strong high frequency component exhibited by the isolated dots. However, since the grid frequency can interact with texture in an image or with other color planes or with a scanning grid, Moire and other undesirable beat patterns can result.
These undesirable patterns can be reduced or eliminated by AM-FM halftoning. AM-FM halftoning involves using stochastic spatial point processes with clusters of dots of variable size and density. Clustered-dot stochastic halftone arrangements produce halftone images exhibiting halftone noise that is very similar to the grain noise in a photograph. These halftone images better resemble real photographs.
An AM-FM halftone screen can be used to render an AM-FM halftone image from a contone image. In general, a halftone screen (also referred to as a dither matrix) consists of a two-dimensional array of thresholds, each threshold having a value v ranging from 0 to (z−1), where z represents the total number of gray levels within the gray scale range being used. For example, 0≦v≦255 on an 8-bit gray scale, where 0 represents white and 255 represents black.
During halftoning of a monochrome image, a halftone screen is typically tiled across a monochrome image. Each pixel of the monochrome image is compared to a spatially corresponding threshold in a halftone screen. If the value of the pixel in the monochrome image is larger than the threshold value, a dot is formed in the corresponding position of the halftone image, assuming an ascending gray scale is employed (i.e., where higher gray levels correspond to darker gray tones).
An AM-FM screen can be designed by selecting cluster centers, and growing the clusters about their centers. The cluster centers can have a stochastic distribution.
A challenge to AM-FM screen design is deciding how to grow the clusters. The clusters should be grown in a manner that provides visually pleasing halftones.
Another challenge is generating a halftone screen that achieves a desired stochastic dot distribution, while minimizing the need for experimentation. One approach towards screen design involves using different filters for each gray level, and then selecting the filter that produces the best results. However, this approach can be time consuming and expensive since there is no explicit connection between the desired distribution and empirical parameters.